Wasserstein Barycenters for more than 1-D distributions
Hi, Thanks for a great tool box. In the example as well in documentation – the method ot.bregman.barycenter(A,M..) calculates the entropic regularized wasserstein barycenter of distributions A where each column of A is considered a distribution implying – that it computes Barycenters for 1-D distributions. I want to ask if there is an easy way to extend this to more than 1-D distributions, say 2 or 3 or to arbitrary dimensions. I have read the convolutional Wasserstein distance paper by Solomon et al (SIGGRAPH 2015). I also want to ask if it will be implemented in this toolbox as well? Thanks Kowshik Thopalli
Hello Kowshik Thopalli, The barycenter implemented in POT can handle any dimensionality if the cost matrix can fit in memory (you can use vectorized 2D images and M should reflect the distance between the vectorized pixels positions) which limits there use for large dimensional histograms. I personally used the function successfully for 2D barycenters of size 32x32. For large 2D and 3D image the Convolutional Barycenters of Solomon et Al is clearly a better fit though because the linear operator applied during the Bergman projection can be computed very efficiently by a convolution (with a large gain in memory and computational efficiency). I know Nicolas Courty has a quick implementation for those barycenters but nothing clean enough to make it into POT yet. But yes we definitely plan to add them to the toolbox in the future. If you make an implementation yourself feel free to contribute it to the toolbox. Rémi Le 05/06/2018 à 21:21, thopalli1@llnl.gov a écrit :
Hi,
Thanks for a great tool box. In the example as well in documentation – the method ot.bregman.barycenter(A,M..) calculates the entropic regularized wasserstein barycenter of distributions A where each column of A is considered a distribution implying – that it computes Barycenters for 1-D distributions.
I want to ask if there is an easy way to extend this to more than 1-D distributions, say 2 or 3 or to arbitrary dimensions.
I have read the convolutional Wasserstein distance paper by Solomon et al (SIGGRAPH 2015). I also want to ask if it will be implemented in this toolbox as well?
Thanks Kowshik Thopalli _______________________________________________ POT mailing list -- pot@python.org To unsubscribe send an email to pot-leave@python.org https://mail.python.org/mm3/mailman3/lists/pot.python.org/
-- Rémi Flamary Web: http://remi.flamary.com Tel: +33 (0)4 92 07 63 80 Laboratoire Lagrange, UMR CNRS 7293 Observatoire de la Côte d'Azur Université de Nice Sophia-Antipolis
Hello Kowshik Thopalli, Yes I have some code for the convolutional barycenters of Solomon et al. but I would need a little bit of time to clean this up and make it compliant to POT standards. If you are interested, please post a feature request on POT’s git, and I will follow up. Cheers, Nicolas
Le 5 juin 2018 à 22:43, Rémi Flamary <remi.flamary@unice.fr> a écrit :
Hello Kowshik Thopalli,
The barycenter implemented in POT can handle any dimensionality if the cost matrix can fit in memory (you can use vectorized 2D images and M should reflect the distance between the vectorized pixels positions) which limits there use for large dimensional histograms. I personally used the function successfully for 2D barycenters of size 32x32.
For large 2D and 3D image the Convolutional Barycenters of Solomon et Al is clearly a better fit though because the linear operator applied during the Bergman projection can be computed very efficiently by a convolution (with a large gain in memory and computational efficiency).
I know Nicolas Courty has a quick implementation for those barycenters but nothing clean enough to make it into POT yet. But yes we definitely plan to add them to the toolbox in the future. If you make an implementation yourself feel free to contribute it to the toolbox.
Rémi
Le 05/06/2018 à 21:21, thopalli1@llnl.gov a écrit :
Hi, Thanks for a great tool box. In the example as well in documentation – the method ot.bregman.barycenter(A,M..) calculates the entropic regularized wasserstein barycenter of distributions A where each column of A is considered a distribution implying – that it computes Barycenters for 1-D distributions. I want to ask if there is an easy way to extend this to more than 1-D distributions, say 2 or 3 or to arbitrary dimensions. I have read the convolutional Wasserstein distance paper by Solomon et al (SIGGRAPH 2015). I also want to ask if it will be implemented in this toolbox as well? Thanks Kowshik Thopalli _______________________________________________ POT mailing list -- pot@python.org To unsubscribe send an email to pot-leave@python.org https://mail.python.org/mm3/mailman3/lists/pot.python.org/
-- Rémi Flamary Web: http://remi.flamary.com Tel: +33 (0)4 92 07 63 80 Laboratoire Lagrange, UMR CNRS 7293 Observatoire de la Côte d'Azur Université de Nice Sophia-Antipolis
_______________________________________________ POT mailing list -- pot@python.org To unsubscribe send an email to pot-leave@python.org https://mail.python.org/mm3/mailman3/lists/pot.python.org/
Thank you. I will try for some 2-D , 3-D simple distributions. I will post a feature request in git asap. Also, I am reading your recent paper- 'Large Scale OT and Mapping estimation'. Cool and sound ideas. Congratulations on it being accepted to ICML 2018. I hope you would release the code for it as well. Thanks Kowshik Thopalli. On 6/5/18, 2:10 PM, "Nicolas Courty" <nicolas.courty@univ-ubs.fr> wrote: Yes I have some code for the convolutional barycenters of Solomon et al. but I would need a little bit of time to clean this up and make it compliant to POT standards. If you are interested, please post a feature request on POT’s git, and I will follow up.
participants (4)
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Nicolas Courty -
Rémi Flamary -
Thopalli, Kowshik -
thopalli1＠llnl.gov